The epimorphism relation among countable groups is a complete analytic quasi-order

TL;DR

The paper establishes that the epimorphism relation among countable groups is a complex, complete analytic quasi-order, and also proves a related completeness result for pointed reflexive graphs.

Contribution

It proves the completeness of the epimorphism relation among countable groups and extends this to pointed reflexive graphs, advancing understanding of their structural complexity.

Findings

Epimorphism relation on countable groups is a complete analytic quasi-order.

Epimorphism relation on pointed reflexive graphs is also complete.

Provides new insights into the complexity of algebraic and graph-theoretic structures.

Abstract

We prove that the epimorphism relation is a complete analytic quasi-order on the space of countable groups. In the process, we obtain the result of independent interest that the epimorphism relation on pointed reflexive graphs is complete.